PART A. INTRODUCORY LINEAR ALGEBRA (Theory and Lab)
Brief presentation of the Algebra of Matrices and of Determinants. Linear Systems
Eigevalues, Eigenvector and the Theorem of Vieta. Cayley-Hamilton Theorem. Spectral Theorem. Linear independence and Base in finite dimensional Linear Spaces. Orthogonal and Orthonormal Bases. Diagonalization Theorem. Primitive roots of unity. The DFT and the FFT.
PART Β. INTRODUCTORY NUMERICAL LINEAR ALGEBRA (Theory and Lab)
- Classical and modified algorithm of Gram-Schmidt.
- Least squares problems and matrices.
- LU and QR factorization of matrices and some of their applications.
- The Gauss-Jordan elimination algorithm (pivoting).
- SVD and its application to data reduction.
- Rotation on the plane and in space.
- The stability problem of Linear Algrbra’s Algorithms